Yes, but not always.
An easy example is sqrt(2) + sqrt(2) + sqrt(2) = 3sqrt(2), an irrational number.
An easy counterexample is 2sqrt(2) + -sqrt(2) + -sqrt(2) = 0, which is rational.
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Yes
Such a sum is always irrational.
The sum of a rational and irrational number must be an irrational number.
Can be rational or irrational.
No. For example, -root(2) + root(2) is zero, which is rational.Note that MOST calculations involving irrational numbers give you an irrational number, but there are a few exceptions.